Henry Ernest Dudeney/Puzzles and Curious Problems/265 - Inspecting the Roads/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $265$

Inspecting the Roads

A man starting from the town $A$, has to inspect throughout all the roads shown from town to town.

Their respective lengths, $13$, $12$, and $5$ miles, are all shown.

What is the shortest route he can adopt, ending his journey wherever he likes?

Solution

The shortest route is $\text {ABCHCDEIEFGBHDIHGIFAG}$.

This traverses all roads once, except $CH$ and $EI$, which are traversed twice.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solution: $265$. -- Inspecting the Roads
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $423$. Inspecting the Roads